What can make an extremist religious leader so confident in their beliefs, no matter how radical and unorthodox those ideas are?

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... To the point where they would follow through with very radical actions? I'm not talking about the con-men who take advantage of people, but the leaders who sincerely mean well and do believe what they believe. What are the psychosocial or environment factors for a person to believe in such an extreme ideology without ever doubting himself?

Because he doesn't think his beliefs are radical or extremist, and most probably doesn't care about judgments of others. That's what I'm thinking of.

Let alone, if he's living in today's world -he will find that cutting someone's head is brutal but bombing about 1.000.000 people is okay. Double standards are every where, what's lawful for X is not lawful for Y. It's okay to preach freedom of whatever, but this freedom is unable to tolerate beliefs of a group of people.

So, may be - just assuming - he decided not to care about how his actions are being perceived.

I'm not saying there is not extremism and radicalism- but it doesn't apply only to religion: it applies to policies, decisions, ways of thinking etc.

There are no such things as extremist religious "leaders" - they are more aptly called tyrannical zealots who make people follow them in fear.

These are "thugs in the whitehouse" so to speak. Not the American whitehouse but a "white" house as in whitewash.  They whitewash all of the greys to make a black and white statement of ideology.  Although they do believe what they say they believe, they do not believe in the nature of their own belief system. They have instead discovered the system, and are working it for the nature of their own power.

There are people who do this on a much smaller scale within a culture, or society, or even the neighborhood. These individuals are deeply depressed on the inside, but on the outside seek the power they lose in their intellectual analysis of the self.

The only way to dislodge these people from power is to completely eliminate their power structure. You cannot take them from power peacefully, because no one is completely sure that the zealot isn't the right leader for better days. In other words, the only reason they come to power is because the powerlessness of a culture is personified in the zealot's message.

It is how Hitler came to power, Stalin, Mussolini.  These are individuals who take the ill of a populace and use it as an opportunity to turn power into a system of self indulgence.

It is why Bush was spiritually guided to dethrone Saddam Hussein. The perfect opportunity arose, but Bush was always going to take him out. It was part of a guidance that came through a mystic early on in his presidency.